Paper by Martin L. Demaine
- Erik D. Demaine, Martin L. Demaine, Goran Konjevod, and Robert J. Lang, “Folding a Better Checkerboard”, in Proceedings of the 20th Annual International Symposium on Algorithms and Computation (ISAAC 2009), Lecture Notes in Computer Science, volume 5878, Hawaii, USA, December 16–18, 2009, pages 1074–1083.
Folding an n × n checkerboard pattern from a
square of paper that is white on one side and black on the other has been
thought for several years to require a paper square of
semiperimeter n2. Indeed, within a restricted class of
foldings that match all previous origami models of this flavor, one can prove
a lower bound of n2 (though a matching upper bound was
not known). We show how to break through this barrier and fold an
n × n checkerboard from a paper square of
semiperimeter ½ n2 + O(n).
In particular, our construction strictly beats semiperimeter
n2 for (even) n > 16, and for
n = 8, we improve on the best seamless folding.
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